Grazing and Strange Attractors Fragmentation in Non-smooth Dynamical Systems

Albert C. J. Luo
Department of Mechanical and Industrial Engineering
Southern Illinois University Edwardsville
Edwardsville, IL 62026-1805

This presentsation will give some new ideas to understand the strange attractor fragmentation caused by grazing in non-smooth dynamic systems. The sufficient and necessary conditions for grazing bifurcations in non-smooth dynamic systems are presented. The initial sets of grazing mapping are introduced and the corresponding initial grazing manifolds are discussed. The grazing-induced fragmentation of strange attractors of chaotic motions in non-smooth dynamical systems is presented. The mathematical theory for such a fragmentation of strange attractors should be further developed.